Mortgage approvals worth £1,735 were made in June, an increase of 11% on the £1,559 million in May and the highest level this year.
Adrian Coles, director-general of the BSA, said: "Activity in the mortgage market has picked up compared to the start of the year, and the rising number of approvals is a positive indicator for coming months.
“However, the forthcoming public sector cuts may add to the economic uncertainty which could constrain any significant growth in mortgage lending in coming months."
In the savings market, balances deposited at mutuals increased by £16 million in June, compared to a reduction of £373 million in May. In the first half of 2010, balances at mutuals increased by £1,445 million. Excluding interest credited to accounts in the month, there was a net withdrawal from mutuals of £262 million in June compared to a net withdrawal of £576 million in May.
Coles added: "Savings balances at mutuals have increased over the first six months of the year which is encouraging given the difficult market conditions that financial institutions face. Yet it will remain challenging to attract savers whilst the Bank Rate remains low and the tough economic climate puts added strain on household finances."